-8x(3x+6)=4-x

Solution for -8x(3x+6)=4-x equation:

Simplifying
-8x(3x + 6) = 4 + -1x

Reorder the terms:
-8x(6 + 3x) = 4 + -1x
(6 * -8x + 3x * -8x) = 4 + -1x
(-48x + -24x2) = 4 + -1x

Solving
-48x + -24x2 = 4 + -1x

Solving for variable 'x'.

Reorder the terms:
-4 + -48x + x + -24x2 = 4 + -1x + -4 + x

Combine like terms: -48x + x = -47x
-4 + -47x + -24x2 = 4 + -1x + -4 + x

Reorder the terms:
-4 + -47x + -24x2 = 4 + -4 + -1x + x

Combine like terms: 4 + -4 = 0
-4 + -47x + -24x2 = 0 + -1x + x
-4 + -47x + -24x2 = -1x + x

Combine like terms: -1x + x = 0
-4 + -47x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 47x + 24x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + 47x + 24x2)' equal to zero and attempt to solve:

Simplifying
4 + 47x + 24x2 = 0

Solving
4 + 47x + 24x2 = 0

Begin completing the square.  Divide all terms by
24 the coefficient of the squared term: 

Divide each side by '24'.
0.1666666667 + 1.958333333x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 1.958333333x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 1.958333333x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 1.958333333x + x2 = 0 + -0.1666666667
1.958333333x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
1.958333333x + x2 = -0.1666666667

The x term is 1.958333333x.  Take half its coefficient (0.9791666665).
Square it (0.9587673608) and add it to both sides.

Add '0.9587673608' to each side of the equation.
1.958333333x + 0.9587673608 + x2 = -0.1666666667 + 0.9587673608

Reorder the terms:
0.9587673608 + 1.958333333x + x2 = -0.1666666667 + 0.9587673608

Combine like terms: -0.1666666667 + 0.9587673608 = 0.7921006941
0.9587673608 + 1.958333333x + x2 = 0.7921006941

Factor a perfect square on the left side:
(x + 0.9791666665)(x + 0.9791666665) = 0.7921006941

Calculate the square root of the right side: 0.89000039

Break this problem into two subproblems by setting 
(x + 0.9791666665) equal to 0.89000039 and -0.89000039.

Subproblem 1
x + 0.9791666665 = 0.89000039

Simplifying
x + 0.9791666665 = 0.89000039

Reorder the terms:
0.9791666665 + x = 0.89000039

Solving
0.9791666665 + x = 0.89000039

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.9791666665' to each side of the equation.
0.9791666665 + -0.9791666665 + x = 0.89000039 + -0.9791666665

Combine like terms: 0.9791666665 + -0.9791666665 = 0.0000000000
0.0000000000 + x = 0.89000039 + -0.9791666665
x = 0.89000039 + -0.9791666665

Combine like terms: 0.89000039 + -0.9791666665 = -0.0891662765
x = -0.0891662765

Simplifying
x = -0.0891662765

Subproblem 2
x + 0.9791666665 = -0.89000039

Simplifying
x + 0.9791666665 = -0.89000039

Reorder the terms:
0.9791666665 + x = -0.89000039

Solving
0.9791666665 + x = -0.89000039

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.9791666665' to each side of the equation.
0.9791666665 + -0.9791666665 + x = -0.89000039 + -0.9791666665

Combine like terms: 0.9791666665 + -0.9791666665 = 0.0000000000
0.0000000000 + x = -0.89000039 + -0.9791666665
x = -0.89000039 + -0.9791666665

Combine like terms: -0.89000039 + -0.9791666665 = -1.8691670565
x = -1.8691670565

Simplifying
x = -1.8691670565

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0891662765, -1.8691670565}
Solution
x = {-0.0891662765, -1.8691670565}